I would not keep my drums in 85 degree heat for too long. Eventually it will harm the wood, the wrap if there is one, and if it is humid like here in Florida, you will ruin them for sure. The heads are the last thing to be worried about.

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Less than 300 days until retirement.
Gretsch Renown

Keep them in a controlled climate that YOU would be comfortable in. Rapid fluctuations in temperature and anything outside of a range of (roughly) 50 to 75 degrees F can have a negative effect on your shells.

These guys speak the truth, so no need to mention anything about the shells.

The heads will be effected by the climate. Mylar was introduced because of this very reason. Calf/goat skin heads were very difficult to keep in tune because of climate changes. The smallest drop in temperature would tighten them up. Hot humid weather would loosen them making them tubby and flat.

You don't see these extremes with mylar, but it does happen. The same thing that happened to calf/goat skin heads happens to mylar. Cold = tight, too warm = lose and flubby.

I used to play in a band that did a lot of hotel night clubs (early '80s, remember playing the Sheraton Hotels, etc..? Those were the days, we actually got paid a half decent wage.) Anyways. We would set up and get sound checks usually pretty early in the day.Our first set started around 9:30pm. Since the clubs were usually empty during the day when we set up, then filled up for happy hour and then it rolled over to dinner and then time for us to play. Many, many times the difference in temperature and humidity would change enough between an empty room and a full room that my drums would need some tunning.

Drums are affected by temp and humidity. I have never known of a drum to be damaged from humidity unless it became totally immersed in a wet condition for a long period of time. I would say that rapid changes in temp and humidity is the worst thing for them. Never leave them in the car overnight. If they get caught in the rain dry them immediately. Mylar drum heads are tough and they change tune slightly, but it takes a lot to ruin a drum head. Marching bands play drums in all sorts of conditions and the heads take it. I wouldn't think that your garage would be a big problem.